5.1. The criterion of effectiveness.
5.2. The choice of methods for probabilistic modeling.

      The beginning of XXI-st century, time of exclusively intensive development of information computer technologies, time of their introduction in all spheres and areas of ability to live of the person. The information really became the same objective reality, as well as subjects surrounding us so, there is an imperative need of working out of equipment rooms and software for its intensive processing that will allow saving time, efforts and material means.

      Particularly relevant is the task of the trade drugs. For commercial enterprises is very important to respond immediately to changing market conditions, prices and other factors affecting the demand of buyers. Medium and large retail chains have a large daily volume of orders, shipments and sales. In such circumstances, an effective solution to the totality of the challenges faced by managers of the company (principal among them are procurement planning, pricing, accounting for inventory movement, financial resources and other economic activities), can provide a computerized information system developed for this purpose.

     A new round of development of the economy of the Palestinian Authority in terms of integration into the World Trade Organization requires the development of new computer technologies that provide a more rational organization of the socio-economic systems (SES) and better management of enterprises, supply the region a variety of goods. One of the most topical areas in this sphere of activity is trade in drugs. This raises the problem of comprehensive market research pharmaceutical products aimed at analyzing the classification of medicines, the identification and assessment of multi-factor in their implementation, and building on the basis of information system management and optimization, which will provide more efficient decision-making when planning the implementation of medicines.

      From the analysis of works devoted to the prediction of demand, it is known that the necessary level of efficiency of decision making in the field of economic problems can be obtained with the help of modern information technology based on mathematical modeling of processes occurring in the market.

     Thus, current scientific challenge is to develop models and algorithms for information systems (IS) demand forecasting and planning the implementation of medicines. The use of IP will allow for the effective management of the implementation through the use of new information technologies. Using the developed models and algorithms ES increase speed and accuracy of decision-making in the implementation of medicines. For this purpose it is necessary to solve the following tasks:

- justification criterion of the effectiveness of decision-making in the management process of the medical products;
- selection and justification of the methods of demand forecasting and modeling of the subject area;
- Develop database to store structured data and knowledge of the subject area;
- creating a mathematical model of multi-factors influence the demand for medical products;
- Building optimization model realization of medicines;
- software development and implementation of expert systems.

     The object of research is the socio-economic subsystem implementation medicines acting on the basis of a collective enterprise TRADE-Medicine, the main area of activity of which is retail and wholesale implementation of medicines. Effective investigation and management of such systems in modern conditions only if the use of new information technologies and methods of scientific knowledge, which occupies a special place a systematic approach.

     With all the features of the system can not accommodate the influence of the external environment. In reality there is absolutely isolated, or separate systems. Effects of environment on the system is manifested in the form of some of the factors identified as affecting the internal state of the system. Impact of environmental factors on the system are called input. In turn, the system is not neutral with respect to the external environment. Its impact on the external environment is characterized by the value of output values.

      Study on the economic position of objects with a systemic approach requires the following work:

1. study of inter-related operational requirements of economic laws that determine the nature and basis for planning;
2. definition of the development of this system from the perspective of a more general system of which it is a criterion for proper formation of optimal planning and operation of the system;
3. a structural analysis system, revealing the nature of relationships and purpose of each subsystem;
4. investigation of control and feedback mechanisms for effective implementation of plans;
5. determine the nature and the impact on the functioning of the system environment (Environment) to improve the reliability of planning decisions.

     Consider the structure of the preseed the economic subsystem and its operation. Graphic model of the system is clearly represented in Figure 1.1. The structure of the system is represented by three subsystems:

• Subsystem sale of goods(SSG);
• Subsystem studies demand(SSD);
• Information Management Subsystem developed.

      Each of the three parts of the system operates autonomously, interacting both among themselves and with the external environment. The algorithm of the system is shown below. The scheme of the algorithm is presented in Figure 1.2. Theory, which relies on this section is addressed in section 1, the mathematical setting of these methods is contained in section 2.

     The operation of the economic sub-systems: continuous-discrete process. It ensures the continuity of the economy, as the economic activities of society. Discreteness process seen in the allocation of such activities in a particular condition, in which the state of the system varies considerably.

      Initial state in this process is to request a subsystem of sale of goods and the balance of ART (0). This joke is SSG massive implementations for a certain period, and at the outlet of ORT played a list of products: primary process, as well as the balance of goods (1).
After this subsystem performs the optimization plan: Based on the data received from the TEC on demand (4) produces a specification of requirements for goods ordered: the first stage of optimization. In doing so, apart from the remainder of the product in the ORT, is taken into account the impact of all significant kvazidinamicheskih factors affecting demand (data from the TEC (4) plus the static factors of protection in the program). Based on the calculation subsystem calculates the plan. However, the plan does not include such goods, the demand for which insignificant.

      Thus, the subsystem has an approved plan of the goods in the amount of maximum eligible needs.
     Next subsystem makes planning the planned procurement of goods. A search for optimal solutions based on data requested from vendors on price and quality of the product (10), as well as the kvazidinamic factors the second stage of optimization. Thus affecting planning (11) sub-optimal plan has a maximum eligible purchases of goods from the relevant suppliers.
     The resulting two optimizations plan to be the translation, that is, purchasing in the market of the goods in the number of relevant suppliers.

Figure 1.2 Block diagram of algorithm of operation of the subsystem

      The final phase of the system of posting is received the goods. This is the third stage of optimization, which, according to the accepted economic methodology, to buy goods planned retail prices. This oprihodovanny product is accompanied by the necessary documentation and is sent on channel 2 in the SSG, which ends the cycle of functioning of the EC. system.

      The frequency of the iterations of this cycle is determined by demand region and is usually once every two days. Globally, this process also relies on non-price factors (see Section 1), which may be required as to increase this frequency (eg, during periods of the epidemic) until two or three times a day, and the reduction (eg summer vacation season and the same holiday period, with falling sales honey. preparations) to three or four days, or even a week. At the same time as a result of each iteration there is a definite economic benefit.

      The system, based on knowledge : These are ACS, which is based on the concept of a knowledge base to generate algorithms for solving economic problems of different classes, depending on the information needs of users. Decision-making using POP to exercise with the help of an expert system.

      Э Expert systems: it is complex software systems, accumulating knowledge of experts in specific fields (PRO), and replicated this empirical evidence for consultations less skilled users. Creating a Power Plant is one of the advanced artificial intelligence areas of science, whose goal is to develop hardware and software tools that allow the user to raise and solve creative tasks, communicating with computers on a limited subset of natural language [3]. Establishment of ES is closely connected with the development of models of knowledge creation and knowledge bases that make up the core of expert systems. Recently, this line gets steady state, involving the use of models and methods for extracting and structuring knowledge, and merges with a relatively young branch of science, the result of a combination of systems analysis and engineering knowledge of cognitive psychology.

      Traditionally, the main supplier of knowledge for the Power Plant is a specialist competent in the subject-defense expert. However, the task of extracting this knowledge is not so trivial as it seems at first glance. Based on the experience gained in the field of automated data processing systems is well known that a lot of knowledge in a particular defense to be the personal property of an expert. The reason is an inability to transmit their expert knowledge and experience because of the proven fact of cognitive psychology - people know much more than himself is aware of [4]. This statement notes the existence of so-called informal or tacit knowledge, associated with a number of factors:

- Part of expertise is not understand the nature;
- An expert is not always able to appreciate the importance of specific knowledge to make a decision, and sometimes even unable to express them;
- The experience of the expert, it is difficult verbalizovat and present in a formalized way.

      Much of the knowledge can be found in the non-strictly defined conditions, which are not updated perceived semantic context. These conditions may be, for example, verbal or nonverbal stimulus, bearing the appropriate semantics, a situation that has an indirect relation to this knowledge, or even accidentally be seen. Thus the knowledge displayed in the consciousness of subject experts, and then can be extracted and formalized by the knowledge engineer.

As noted in section 1, the optimization is conducted on the socio-economic indicators:

(3.1)

Minimizing the time of service the consumer L applications:

(3.2)

Improving the accuracy of product offers the nomenclature M units:

(3.3)

      The values of 3.1 - 3.3 are calculated for each commercial unit in a particular paragraph implementation, which are aggregated in the summary indicators and relevant to the chemist's point. In addition, tasks 3.1 and 3.2 relate to the modeling of queuing systems. The last three challenges to the use of economic-mathematical methods of evaluation, which in themselves do not represent the values in the problem of optimization, but their integration with the methods veroyanostnoy evaluation factors is of great scientific interest.

      Complex systems are always exposed to a variety of factors, both external and internal. This change in one factor is the direct cause of changes in other, sometimes very many factors. Such systems always have some probabilistic structure, and, hence, are described using probabilistic methods. Below are the Monte Carlo method, based on the simulation of random events, tailored to the social processes that are highly complex and certainly include stochastic components [18]. Here c to explore relations in the stochastic process of justified use of simulation and the theory of queuing systems, where system characteristics are specified probability distributions (modeling continuous factors), Markov chains (discrete parameterization of objects and relations) and matrices of transition probabilities (the realization of relations between objects ). Modeled using such methods, the information process in a flexible (intellectually) the mechanism of the parameterization of the knowledge-based expert, it is sufficiently homomorphism actual process of implementation. Thus, the developed simulation model will not only obtain the best characteristics of the modeled process, but will be one of the subsystems developed by an expert system, the main purpose of which is the formation of the field of acceptable solutions generated by ES.

      Genetic algorithms (GA): adaptive search methods that have recently often used for solving functional optimization. Imitating the natural process of evolution, genetic algorithms are able to "develop solutions to real problems if they are adequately encrypted. The classical GA uses a direct analogy with the natural mechanisms. They work with a combined population of individuals, each of which represents a possible solution to this problem. Each specimen is estimated measure of its fitness according to how the best match to the task. The combination of well-chosen operators provide high-quality evolyutsionirovanie individuals [19]. In the general case is considered continuous Multiparametric continuous optimization problem:

where f (x) maxim (task) multi parametrical scalar function, which can not be defined out of the area, but within the permissible area of a few global extreme; rectangular area D search. It is assumed that the function f (x) is known only that it is defined anywhere in the area D. No additional information about the nature of the function and its properties (differentiability, continuity, etc.) are not included in the search process. Under the task will be to understand the vector x = (x1, x2, ..., xN). The optimal decision problem will take a vector x *, where the function f (x) takes the maximum value. Assuming a possible Multiple f (x), the optimal solution may not be the only one.

     There are at least three classes of tasks that can be solved by the algorithm presented by [20]. First, it is the task of rapid containment of an optimal solution, and second, under certain conditions, may find a few (or all) of global extrema, and the third is the use of an algorithm for mapping landscape functions investigated.

      GA work with a collection of individuals-solutions: the population, each of which represents a possible solution to this problem. Each specimen is estimated measure of its "fitness" according to how well relevant to the task. The most adapted species are able to be involved in the further operation of the GA. This leads to the emergence of new species, which combine some characteristics inherited from their parents. Sometimes the mutations are occurring, or spontaneous changes in genes.

      Т Thus, from generation to generation, the characteristics necessary for the development, distributed throughout the population. Crossing of the fittest individuals has meant that explores the most promising areas of search space. Eventually the population will converge to the optimal solution of the problem. The advantage of GA is that it is approximately optimal solutions in a relatively short period of time [21].

GA consists of the following components:
- Gen. Encrypted value of quality factor (trait).
- Chromosome. The solution of the problem. Initial population of chromosomes
- A set of operators to generate new solutions from the previous population.
- Fitness function (FY) obviously unsuitable for screening decisions.
- Objective function (TF) to assess the fitness (fitness) solutions.

     The last two components of the algorithm focused on the selection: FG - artificial, TF - natural. FG can not be used, which slows the convergence but also ensure a smooth development.

     The operating principle of the genetic algorithms based on modeling the mechanisms of population genetics:

- chromosome set manipulation in the formation of a new genotype of the biological species through the succession of sites of chromosomal sets of parents krossingover;
- random changes in genotype, known as a mutation in nature;
- inversion operator, which is that the chromosome is divided into two parts, and then they switch places;
- process of natural selection, aimed at improving the fitness of members of the population by a greater ability to "survive" individuals who possess the best traits.

      The most useful data are obtained by specialists in the analysis of fuzzy uncertainty (Figure 3.1), where the main feature is the need for payments when there are not clearly defined parameters or inaccurate information technology. For the treatment of inaccurately known values usually applied theory of probability. But randomness is related to uncertainty, which refers to some object belonging to the normal set. This discrepancy between the ambiguity and coincidence leads to the fact that the mathematical methods of fuzzy sets, in many respects, easier methods of probability theory by the fact that the notion of a probabilistic measure of the probability theory with the simpler notion of function accessories (OP) in the theory of fuzzy sets. It is therefore more convenient to operate with uncertainty methods of the theory of fuzzy sets without the involvement of the classical theory of probability. The theoretical foundation of this approach is entirely accurate and rigorous in the mathematical meaning and are not in themselves a source of uncertainty. In each case, the accuracy of solutions could be coherent with the objectives and accuracy of available data. Such flexibility is one of the important features of the method, details below.

      In-depth study of the company reveals many sources of uncertainty, while a number of parameters can not be measured accurately, and then in his assessment inevitably a subjective component, which is vague estimates of "high", the "most acceptable", "very expected," "likely" "unlikely", "not" and so on. Appears that the science is described as a linguistic variable with its term-set of values, and communication of quantitative values of certain factors in its high-quality linguistic description is given by the OP. It is a quantitative measure of uncertainty about these parameters, the values of which are described μ_А(u) - a function whose domain is the media U, a range of values - the unit interval [0, 1]. The higher the higher the estimated level of vehicle ownership element u fuzzy set A.

Figure 3.1 Graph functions of fuzzy subsets supplies «The optimal age for the consumer»

(2.17)

where Ω - the name of the variable; term-set of values; U: drive; G: syntax rules, producing the set of terms T, M: semantic rule that each linguistic value put in the line of its contents М(ω), with М(ω) denotes the fuzzy subset of U.

      Например, зададим ЛП Q = "Возраст потребителя". Определим синтаксическое правило G как определение "оптимальный", что накладывается на переменную Q. Тогда полное терм-множество значений Т = {Т1 = Оптимальный возраст потребителя, Т2 = Неоптимальный возраст потребителя}. Носителем U выступает отрезок [0, 110], измеренный в летах человеческой жизни. На этом носители определены две функции принадлежности: для значения Т₁ - μ_T1(u).

      Fuzzy numbers in this problem of demand forecasting can be of three types (Figure 3.2), define a discrete, discrete-continuous and continuous μ(x). Discrete characterization is given by a functions belonging linear relationship. Two popular versions of these dependencies: triangular (a) and trapezoidal (c) OP.

Figure 2.10 Options for ways to present the fuzzy numbers

  Function belonging to the triangular number is defined according to expression (3.5). Here at а ± δ ≈ а in descending order δ degree of confidence in the assessment increases to unity. This gives the OP a triangular appearance (malyunok 3.2), with a degree of approximation are the expert.

(3.5)

      Triangular numbers: it is the most frequently used in practice, the type of fuzzy numbers are often as predictive values of this parameter.

      Trapezoidal membership function for the number (Figure 3.2 in) is determined in accordance with expression (3.6). Here the subject of peer review (the fuzzy classification) is about average. In [23] justified that the trapezoidal numbers - the most natural way uncertain classification.

(3.6)

      The next two common variants of the fuzzy set of numbers, respectively, discrete-continuous and continuous characteristic quantities. In the first case, the U-shaped smooth function (Figure 3.2 g), expressed by nonlinearly discrete functions as arguments. Example of an analytical expression of the function (3.7). The function of this type of fitting used in the presence of break points in the third kind, known as fixed a few states in which an object behaves in a stable and fuzzy границі move an object from one area to another state. Such systems are called discrete-continuous [24].

(3.7)

      Gaussian type membership function (Figure 3.2, b) is a classic example of a continuous OP. Analytical record Gaussian function defined by expression (3.8):

(3.8)

      As a result of the study revealed that planning for the implementation of medicines under the existing information system at the Palestine is far from being the best possible way. Practice of operation in terms of IP showed that the maintenance of records in the database implementations, and making decisions based on the subjective views of the managers could not provide an acceptable cost-effectiveness. From the results it became clear that the problem of meeting the needs of Palestine exists not only among the population, but also in areas of the country's health institutions. Regular interruptions in the supply and the inaccuracy of cause deterioration of medical care of people, which also negatively affects the social situation in Palestine.

      Based on an analysis of the market of medical preparations in the territory of Palestine and the review of existing software solutions for the automation of demand forecasting and decision support to the conclusion of the need to develop on the basis of the existing IP Intellectual automated system (AIS), decision support, using as an information resource of expertise on the subject areas of the market situation and its dynamics [5].

      Analysis methods, models and algorithms allows for research in this area of the following groups:

- machine fuzzy logic that is used for fuzzy modeling and analysis of input data and knowledge of experts, and presenting them in a database and knowledge - the main core of the AIS [5, 7, 22-25];
- mathematical modeling of queuing, functionally representing the process of implementing, operating, and fuzzy models to get a reliable picture of the implementation of medicines at a certain time interval [1, 14, 18];
- methods and technologies of intelligent user interface to interact effectively with the AIS and receive advice and solutions for purchasing, pricing and strategy for implementation of medicines [3, 6, 25].

      Using the mathematical apparatus and their applications, and special software developed by the AIS decision support, providing a positive economic effect on the company and the positive socio-economic impact in the market medications Palestine at the expense of quality to meet the needs of medical institutions and the population in medical preparations.

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